This invention relates to a method of localizing precisely a moving body such as a ship, an automobile, an artificial satellite, etc., and more specifically to a method of localizing a moving body as mentioned above with high precision by receiving energy of radiations, such as acoustic waves, electromagnetic waves, etc., emitted the moving body by using a plurality of sensors disposed at different places and on the basis of reception times measured by the plurality of sensors; or, in the alternative, by receiving energy of radiations, such as acoustic wave, electromagnetic wave, etc. emitted at a plurality of different places using a sensor disposed on the moving body and on the basis of reception times measured by the sensor.
Heretofore, in order to estimate the location of a moving body, e.g. as indicated in FIG. 1, radiations, such as acoustic wave, electromagnetic wave, etc. emitted by a moving body 1 are received by a plurality of sensors S.sub.i (i=1, 2, . . . , n) disposed at different places, which are respectively at a distance d.sub.i from the moving body, at a time t.sub.i, respectively. A moving body localization calculation device 2, receives the radiations detected by the sensors, and calculates an estimated location of the moving body by the least-squares method. It is well known that the representative methods of realizing this estimation are the spherical surface localization method and the hyperbolic surface localization method. These localization methods are described in e.g. "Localization Method in Vehicle Automation" by Tsumura, System and Control, Vol. 25, No. 3 (1981).
In FIG. 1, the moving body localization calculation device 2 consists of a memory device 3, a processing device 4 and a display device 5. Radiation emitted by the moving body 1 is received by a sensor S.sub.i, which is at a distance d.sub.i therefrom. The sensor S.sub.i transmits the time t.sub.i, at which the radiation is received, to the moving body localization calculation device 2. The reception time t.sub.i satisfies the following equation (1). EQU t.sub.i =d.sub.i /Ve+T+n.sub.i ( 1)
where Ve designates the propagation velocity of the radiation, T represents the emission time of the radiation by the moving body 1, and n.sub.i denotes noises due to various factors, such as measurement errors, propagation delay of the wave, etc.
The signal emitted by the moving body 1 is a pulse signal as indicated in FIG. 2, where it is supposed that the time interval between two successive pulses T.sub.o is constant. It is also supposed that the time interval T.sub.o is sufficiently long with respect to the propagation time of the radiation.
In the moving body localization calculation device 2, input data are once stored in the memory device 3. Then the processing device 4 calculates the location of the moving body and outputs the obtained results to the display device 5. In the processing device the position (.alpha..sub.i, .beta..sub.i, .gamma..sub.i) of the sensor S.sub.i, which was measured beforehand, is stored so that it is ready to be utilized.
The hyperbolic surface localization method is a method, by which an intersecting point of a plurality of hyperbolic surfaces in a space, where the difference between two reception times in constant, is assumed to be the position of the moving body and is determined using time differences between two receptions of the radiation by the plurality of sensors. That is, representing the position of the moving body by (x, y, z), for sensors S.sub.i and S.sub.j, the following non-linear equation is valid. ##EQU1## where i, j=1, 2, . . . , n (i.noteq.j). Then, (x, y, z) are determined by the non-linear least-squares method so that the following value (equation (3)) is minimum. ##EQU2##
On the other hand, the spherical surface localization method is a method, by which assuming that the emission time of the radiation from the moving body is known, an intercepting point of a plurality of spherical surfaces is assumed to be the position of the moving body, where the propagation time of the radiation from each of the sensors is constant. That is, assuming that the emission time T of the radiation from the moving body is known, the following non-linear equation is valid. ##EQU3## where i=1, 2, . . . , n. Then, (x, y, z) are determined by the non-linear least-squares method so that the value ##EQU4## is minimum.
Since both the methods described above are based on the method of least squares, they can remove random errors n.sub.i, n.sub.j such as measurement errors, however, they cannot remove bias errors, i.e. systematic errors due to erroneous quantities, such as measurement errors on the position of the sensors (.alpha..sub.i, .beta..sub.i, .gamma..sub.i), deviations from the expected value of the propagation velocity Ve of the radiation, etc. These bias errors cause different error for the 2 localization methods using the least-squares method, e.g. for the hyperbolic surface localization method and the spherical surface localization method and as indicated in FIG. 3, even if identical measured data are used, the estimated location of the moving body differs depending on what localization method is used and, according to circumstances, this difference can be considerably great.
Furthermore, by the hyperbolic surface localization method, it is difficult to determine the time for the calculated position of the moving body. Another problem is that a localization calculation of the hyperbolic surface localization method requires a long processing time. To the contrary, by the spherical surface localization method, although a processing time for a localization calculation is shorter, it cannot be used, unless the emission time of the radiation is known. Thus, either one of the localization methods described above gives a high precision in the localization of a moving body, depending on the geometrical relation between the moving body and the group of sensors. However, since both the localization methods have various restrictive conditions, in practice, these restrictive conditions must be taken into account. The choice of either one of the localization methods is not an important problem for a system in which error factors concerning the propagation of the radiation, such as an acoustic wave, an electromagnetic wave, etc. are small, but it is an important problem for a system requiring high precision, for which error factors concerning the propagation of the radiation are great.